Let's solve the equation step by step:

### Step 1: Simplify the equation
First, combine like terms on the right side of the equation:
\[
3x + 1 - x - 7 = 2x - 6
\]
So, the equation becomes:
\[
2x - 6 = 2x - 6
\]

### Step 2: Subtract \(2x\) from both sides
\[
2x - 6 - 2x = 2x - 6 - 2x
\]
This simplifies to:
\[
-6 = -6
\]

### Conclusion:
The equation simplifies to a true statement, \(-6 = -6\), which means that the original equation is true for **any value of \(x\)**.

Thus, the solution is **all real numbers**.

Would you like more details or have any questions about this solution?

Here are 5 related questions you might find interesting:
1. How do you solve an equation with variables on both sides?
2. What does it mean when an equation has infinitely many solutions?
3. How can you determine when an equation has no solution?
4. What are the steps to solve a quadratic equation?
5. How do you solve a system of linear equations?

**Tip:** Always simplify the equation as much as possible before attempting to solve it.

Learn how to solve the equation 2x - 6 = 3x + 1 - x - 7 with a step-by-step solution. This problem involves combining like terms and solving linear equations. Suitable for students in Grades 6-8.

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